Ah okay! Well, using the pick is a no-no! I use the index finger of my right hand to tap the necessary fret. (That's important, make sure to tap the string right
Down to the fret!)
A good song to learn to practise tapping is "Eruption" by Van Halen. It's not that hard, and really does help your technique.
I found this for you;
http://www.cyberfret.com/techniques/right-hand-tapping/index.php
There are videos attached so you can actually SEE what you're meant to be doing, which may be better than my paltry explanation!
Actually, their definition of taps being like hammer-ons with the right hand is a good one. That's basically what you're doing, a fast hammer-on/pull-off with your right hand as your left plays.